Finite Group Databasebeta

← C127×#13658 #44577331

Subgroups — C127×#13658 #44577331

Order 32512.

194 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#2263C211yesmaximal, characteristic
2C127×#2179C211yesmaximal, characteristic, complemented
3C127×#2177C211yesmaximal, characteristic, complemented
4C127×#1426C211yesmaximal, characteristic, complemented
5C127×#1419C211yesmaximal, characteristic, complemented
6C127×#1418C211yesmaximal, characteristic, complemented
7C127×#1398C211yesmaximal, characteristic, complemented
8#508×C127C2211yescharacteristic
9C2×D16×C127C2211yescharacteristic
10#443×C127—21no—
11C4×D8×C127—21no—
12SD64×C127C412yescomplemented
13D32×C127C412yescomplemented
14M64×C127C2211yescharacteristic
15M64×C127C2211yescharacteristic
16#368×C127C2211yescharacteristic
17#367×C127C2211yescharacteristic
18#359×C127—21no—
19#357×C127—21no—
20#346×C127C2211yescharacteristic
21#135×C127—21no—
22C2×D8×C127—21no—
23#131×C127—41no—
24C4×D4×C127—41no—
25Q32×C127C2×C411yescharacteristic, complemented
26SD32×C127—21no—
27D16×C127—21no—
28D16×C127C2×C412yes—
29D16×C127C2×C411yescharacteristic, complemented
30C2×C16×C127D411yescharacteristic
31C2×C16×C127C2311yescharacteristic
32#108×C127—21no—
33#107×C127—21no—
34#104×C127—41no—
35#102×C127—41no—
36C4×C8×C127D411yescharacteristic
37C32×C127—21no—
38C32×C127C2×C412yescomplemented
39#41×C127—41no—
40C2×D4×C127—41no—
41C22×C4×C127—81no—
42Q16×C127—21no—
43SD16×C127—41no—
44D8×C127—22no—
45D8×C127—21no—
46D8×C127—41no—
47M16×C127—41no—
48M16×C127—81no—
49C2×C8×C127—81no—
50C2×C8×C127D811yescharacteristic
51C2×C8×C127C2×D411yescharacteristic
52C4⋊C4×C127—41no—
53C22⋊C4×C127—81no—
54C42×C127D811yescharacteristic
55C16×C127—21no—
56C16×C127C22×C411yescharacteristic
57C16×C127#4111yescharacteristic
58C23×C127—81no—
59Q8×C127—41no—
60D4×C127—42no—
61D4×C127—41no—
62D4×C127—81no—
63D4×C127—81no—
64C2×C4×C127—21no—
65C2×C4×C127—81no—
66C2×C4×C127—81no—
67C2×C4×C127—162no—
68C2×C4×C127C2×D811yescharacteristic
69C8×C127—21no—
70C8×C127—81no—
71C8×C127C4×D411yescharacteristic
72C8×C127#13511yescharacteristic
73C22×C127—81no—
74C22×C127—82no—
75C22×C127—161no—
76C22×C127—161no—
77C22×C127#50911yescharacteristic
78C4×C127—41no—
79C4×C127—81no—
80C4×C127—161no—
81C4×C127C4×D811yescharacteristic
82C4×C127#50911yescharacteristic
83#13658C12711yesmaximal, characteristic, direct product factor, Sylow
84C2×C127—21no—
85C2×C127—161no—
86C2×C127—162no—
87C2×C127#217711yescharacteristic
88#2263C2×C12711yescharacteristic
89#2179C2×C12711yescharacteristic, complemented
90#2177C2×C12711yescharacteristic, complemented
91#1426C2×C12711yescharacteristic, complemented
92#1419C2×C12711yescharacteristic, complemented
93#1418C2×C12711yescharacteristic, complemented
94#1398C2×C12711yescharacteristic, complemented
95C127#1365811yescharacteristic, direct product factor, Sylow
96#508C22×C12711yescharacteristic
97C2×D16C22×C12711yescharacteristic
98#443—21no—
99C4×D8—21no—
100SD64C4×C12712yescomplemented
101D32C4×C12712yescomplemented
102M64C22×C12711yescharacteristic
103M64C22×C12711yescharacteristic
104#368C22×C12711yescharacteristic
105#367C22×C12711yescharacteristic
106#359—21no—
107#357—21no—
108#346C22×C12711yescharacteristic
109#135—21no—
110C2×D8—21no—
111#131—41no—
112C4×D4—41no—
113Q32C2×C4×C12711yescharacteristic, complemented
114SD32—21no—
115D16—21no—
116D16C2×C4×C12712yes—
117D16C2×C4×C12711yescharacteristic, complemented
118C2×C16D4×C12711yescharacteristic
119C2×C16C23×C12711yescharacteristic
120#108—21no—
121#107—21no—
122#104—41no—
123#102—41no—
124C4×C8D4×C12711yescharacteristic
125C32—21no—
126C32C2×C4×C12712yescomplemented
127#41—41no—
128C2×D4—41no—
129C22×C4—81no—
130Q16—21no—
131SD16—41no—
132D8—22no—
133D8—21no—
134D8—41no—
135M16—41no—
136M16—81no—
137C2×C8—81no—
138C2×C8D8×C12711yescharacteristic
139C2×C8C2×D4×C12711yescharacteristic
140C4⋊C4—41no—
141C22⋊C4—81no—
142C42D8×C12711yescharacteristic
143C16—21no—
144C16C22×C4×C12711yescharacteristic
145C16#41×C12711yescharacteristic
146C23—81no—
147Q8—41no—
148D4—42no—
149D4—41no—
150D4—81no—
151D4—81no—
152C2×C4—21no—
153C2×C4—81no—
154C2×C4—81no—
155C2×C4—162no—
156C2×C4C2×D8×C12711yescharacteristic
157C8—21no—
158C8—81no—
159C8C4×D4×C12711yescharacteristic
160C8#135×C12711yescharacteristic
161C22—81no—
162C22—82no—
163C22—161no—
164C22—161no—
165C22#509×C12711yescharacteristic
166C4—41no—
167C4—81no—
168C4—161no—
169C4C4×D8×C12711yescharacteristic
170C4#509×C12711yescharacteristic
171C2—21no—
172C2—162no—
173C2—161no—
174C2C127×#217711yescharacteristic
subgroupG/H
center, socleC2×C127#2177
commutatorC16C22×C4×C127
Frattini, cosocleC2×C16C23×C127
prime radicalC127×#2263C2
LCSG ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C127 ◁ C2×C4×C127 ◁ C4×C8×C127 ◁ #346×C127 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C127×#2179C2semidirect
3. C127×#2177C2semidirect
4. C127×#1426C2semidirect
5. C127×#1419C2semidirect
6. C127×#1418C2semidirect
7. C127×#1398C2semidirect
12. SD64×C127C4semidirect
13. D32×C127C4semidirect
25. Q32×C127C2×C4semidirect
29. D16×C127C2×C4semidirect
38. C32×C127C2×C4semidirect
83. #13658C127direct (N × H)
89. #2179C2×C127semidirect
90. #2177C2×C127semidirect
91. #1426C2×C127semidirect
92. #1419C2×C127semidirect
93. #1418C2×C127semidirect
94. #1398C2×C127semidirect
95. C127#13658direct (N × H)
100. SD64C4×C127semidirect
101. D32C4×C127semidirect
113. Q32C2×C4×C127semidirect
117. D16C2×C4×C127semidirect
126. C32C2×C4×C127semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C127×#22632
C127×#21792
C127×#21772
C127×#14262
C127×#14192
C127×#14182
C127×#13982
#13658127